Near the end of Chapter 2, two different kinds of standard
scores are discussed: z-scores and T-scores. These are the kinds of standard
scores you're most likely to come across in statistically-based research
studies. However, there's one other kind of standard score that appears
every once in a while. It is called a "stanine score." The purpose
of this message is to explain this third kind of standard score so you
are not thrown by a researcher who refers to stanine scores in his/her
research report.

Like z-scores and T-scores, a stanine score is simply
a way of indicating the position of a person in a group relative to the
other people (or things) that have been measured. Given a person's stanine
scores, we'll know whether he/she scored near the group's mean, above
the group's mean, or below the group's mean. Furthermore, we'll have a
sense for how far above-average or below-average a person scored if he/she
did not score near the mean.

The main difference between z-score and T-scores, on
the one hand, and stanine scores, on the other, is the way these standard
scores are expressed. As you know, z-scores are expressed via decimal
numbers (e.g., z = 1.40) that can be positive or negative, while T-scores
are expressed via 2-digit whole numbers (e.g. T = 64) that are always
positive numbers. Stanine scores are simpler, for they are expressed via
1-digit whole numbers.

A stanine score can be any number between 1 and 9 (inclusive).
Typically, a person is said to be "average" (i.e., near the
mean) if his/her stanine score is a 4, 5, or 6. Stanine scores of 7 or
8 are usually interpreted as indicating "above average" performance.
And a stanine score of 9 is normally considered to reflect "outstanding"
performance, for that's the highest score one can get. As you might suspect,
stanine scores of 2 or 3 are usually interpreted to mean that someone
is "below average," while a stanine score of 1 indicates a relative
position that's "very low."

When stanine scores are associated with test scores
that have been "normalized" (as is usually the case), there
are two additional things about stanines worth knowing. Both of these
additional pieces of information are easier to grasp if you'll think of
a normal curve that's cut up into parts by slicing the bell-shaped curve
8 times in a vertical direction. These 8 "cuts" will create
9 sections of the curve, and they can be numbered from 1 to 9 starting
from the left side of the curve. Your stanine score would be determined
by the section you're in after the curve is cut up in this manner.

The first of the two new things to know about stanine
scores is the percentage of people who will receive any given stanine.
These percentages are as follows: 4% will be in stanine 1, 7% will be
in stanine 2, 12% will be in stanine 3, 17% will be in stanine 4 20% will
bein stanine 5, 17% will be in stanine 6, 12% will be in stanine 7, 7%
willbe in stanine 8, and 4% will be in stanine 9.

The second thing to know about stanines concerns the
"boundary lines" (on the baseline under the normal curve) between
adjacent stanines. These boundary lines are usually expressed via z-scores,
and they are easy to remember if you'll simply memorize the fact that
all stanines except the upper and lower ones have a "width"
(on the baseline under the curve) equal to one-half of a standard deviation.
Thus, the boundaries for stanine 5--the middle section of our cut-up distribution--are
equal to -.25 and +.25. (These z-scores, of course, correspond with the
upper boundary of stanine 4 and the lower boundary of stanine 6, respectively.)

To get the other boundaries, successively add .50 to
stanine 5's upper boundary to get the upper boundaries for for stanines
6, 7, and 8; or, if you successively subtract .50 from stanine 5's lower
boundary, you'll get the lower boundaries of stanines 4, 3, and 2. There
is no upper boundary for stanine 9 and no lower boundary for stanine 1
because the normal curve, in theory, extends forever out toward positive
and negative infinity.

Let me add one final comment before closing. The advantage
of stanines is also the disadvantage of stanines! Because they are expressed
in single-digit whole numbers, stanines carry with them a meaning that
can be learned in about 30 seconds. As indicated earlier, a stanine score
of 4 indicates that someone performed "about average," while
a stanine score of 8 indicates that someone performed well above average.

The fact that stanines are so easy to learn (as compared
with z-scores and T-scores) is offset by the major liability of stanines:
their imprecision. Because everyone in the same section of the cut-up
distribution receives the same stanine score, differences among those
people are "lost" as we convert to stanine scores from raw scores,
z-scores, or T-scores. For example, everyone with a z-score between -.25
and +.25 ends up with the same stanine score. Because stanine 5 contains
20% of the full group, this means that two people with percentile ranks
of 41 and 59 will end up looking alike in terms of stanines. This limitation
of stanines is referred to as a "loss of information."

OK. I'm finally done! Thanks for reading this entire
message. If email messages were measured in terms of their length, I'm
afraid this one would end up with a stanine score of 9! However, I hope
it's given you a feel for what stanine scores are and how to interpret
them.

Sky Huck

P.S. As a little "self-test" to see if you
understand stanines, try to figure out which of these 5 people performed
best on a test that yields scores that are bell-shaped with a mean of
48 and a standard deviation of 4: